# [Numpy-discussion] Optical autocorrelation calculated with numpy is slow

Jochen S cycomanic@gmail....
Tue Mar 31 02:54:36 CDT 2009

```On Tue, Mar 31, 2009 at 7:13 AM, João Luís Silva <jsilva@fc.up.pt> wrote:

> Hi,
>

> I wrote a script to calculate the *optical* autocorrelation of an
> electric field. It's like the autocorrelation, but sums the fields
> instead of multiplying them. I'm calculating
>
> I(tau) = integral( abs(E(t)+E(t-tau))**2,t=-inf..inf)
>

An autocorrelation is just a convolution, which is a multiplication in
frequency space. Thus you can do:
FT_E = fft(E)
FT_ac=FT_E*FT_E.conj()
ac = fftshift(ifft(FT_ac))

where E is your field and ac is your autocorrelation. Also what sort of
autocorrelation are you talking about. For instance SHG autocorrelation is
an intensity autocorrelation thus the first line should be:
FT_E = fft(abs(E)**2)

HTH
Jochen

> with script appended at the end. It's too slow for my purposes (takes ~5
> seconds, and scales ~O(N**2)). numpy's correlate is fast enough, but
> isn't what I need as it multiplies instead of add the fields. Could you
> help me get this script to run faster (without having to write it in
> another programming language) ?
>
> Thanks,
> João Silva
>
> #--------------------------------------------------------
>
> import numpy as np
> #import matplotlib.pyplot as plt
>
> n = 2**12
> n_autocorr = 3*n-2
>
> c = 3E2
> w0 = 2.0*np.pi*c/800.0
> t_max = 100.0
> t = np.linspace(-t_max/2.0,t_max/2.0,n)
>
> E = np.exp(-(t/10.0)**2)*np.exp(1j*w0*t)    #Electric field
>
> dt = t[1]-t[0]
> t_autocorr=np.linspace(-dt*n_autocorr/2.0,dt*n_autocorr/2.0,n_autocorr)
> E1 = np.zeros(n_autocorr,dtype=E.dtype)
> E2 = np.zeros(n_autocorr,dtype=E.dtype)
> Ac = np.zeros(n_autocorr,dtype=np.float64)
>
> E2[n-1:n-1+n] = E[:]
>
> for i in range(2*n-2):
>     E1[:] = 0.0
>     E1[i:i+n] = E[:]
>
>     Ac[i] = np.sum(np.abs(E1+E2)**2)
>
> Ac *= dt
>
> #plt.plot(t_autocorr,Ac)
> #plt.show()
>
> #--------------------------------------------------------
>
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>
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